docs: def Idelchik(dp, voidage, vs, rho, mu, L=1):
      r'''Calculates pressure drop across a packed bed of spheres as in [2]_,
      originally in [1]_.
  
      .. math::
          \frac{\Delta P}{L\rho v_s^2} d_p  = \frac{0.765}{\epsilon^{4.2}}
          \left(\frac{30}{Re_l} + \frac{3}{Re_l^{0.7}} + 0.3\right)
  
      .. math::
          Re_l = (0.45/\epsilon^{0.5})Re_{Erg}
  
      .. math::
          Re_{Erg} = \frac{\rho v_s  D_p}{\mu(1-\epsilon)}
  
      Parameters
      ----------
      dp : float
          Particle diameter of spheres [m]
      voidage : float
          Void fraction of bed packing [-]
      vs : float
          Superficial velocity of the fluid (volumetric flow rate/cross-sectional 
          area)[m/s]
      rho : float
          Density of the fluid [kg/m^3]
      mu : float
          Viscosity of the fluid, [Pa*s]
      L : float, optional
          Length the fluid flows in the packed bed [m]
  
      Returns
      -------
      dP : float
          Pressure drop across the bed [Pa]
  
      Notes
      -----
      :math:`0.001 < Re_{Erg} <1000`
      This equation is valid for void fractions between 0.3 and 0.8. Cited as
      by Bernshtein.
  
      Examples
      --------
      >>> Idelchik(dp=8E-4, voidage=0.4, vs=1E-3, rho=1E3, mu=1E-3)
      1571.909125999067
  
      References
      ----------
      .. [1] Idelchik, I. E. Flow Resistance: A Design Guide for Engineers.
         Hemisphere Publishing Corporation, New York, 1989.
      .. [2] Allen, K. G., T. W. von Backstrom, and D. G. Kroger. "Packed Bed
         Pressure Drop Dependence on Particle Shape, Size Distribution, Packing
         Arrangement and Roughness." Powder Technology 246 (September 2013):
         590-600. doi:10.1016/j.powtec.2013.06.022.
      '''
      Re = rho*vs*dp/mu/(1-voidage)
      Re = (0.45/voidage**0.5)*Re
      right = 0.765/voidage**4.2*(30./Re + 3./Re**0.7 + 0.3)
      left = dp/L/rho/vs**2
      return right/left